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NCERT Class 12 · Ch 13 Exercise 13.3 · Q7

NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 7

An insurer covers 2000 scooter,4000 car,6000 truck drivers, with accident rates 0.01,0.03,0.15. Given an accident, find P(scooter).
Exercise 13.3 Q7: priors, likelihoods and joints
Exercise 13.3 Q7: priors, likelihoods and joints

💡 Concept Hints

  1. Define the events and identify which event is being conditioned on.
  2. Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.

✅ Step-by-Step Solution

Final Answer: scooter: 1/52
  1. Use the mutually exclusive source events with prior probabilities scooter=1/6, car=1/3, truck=1/2.
  2. The observation likelihoods in the same order are 1/100, 3/100, 3/20. Multiply each prior by its likelihood to get joint probabilities 1/600, 1/100, 3/40.
  3. Total probability of the observation is 1/600 + 1/100 + 3/40 = 13/150.
  4. Bayes: P(scooter | observation) = 1/600 / 13/150 = 1/52.

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